Express this quotient in scientific notation: ${\frac{1.080\times 10^{-2}} {2.0\times 10^{-5}}}$
Solution: Start by collecting like terms together. $= {\frac{1.080} {2.0}} \times{\frac{10^{-2}} {10^{-5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.54 \times 10^{-2\,-\,-5}$ $= 0.54 \times 10^{3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.54$ is the same as $5.40 \div 10$ , or $5.40 \times 10^{-1}$ $ = {5.40 \times 10^{-1}} \times 10^{3} $ $= 5.40\times 10^{2}$